Scientific Series

Anderson localization emerges in quantum systems when randomised parameters cause the exponential suppression of motion. In this talk we will consider the localization phenomenon in the toric code, demonstrating its ability to sustain quantum information in a fault tolerant way. We show that an external magnetic field induces quantum walks of anyons, causing logical information to be destroyed in a time linear with the system size when even a single pair of anyons is present. However, by taking into account the disorder inherent in any physical realisation of the code, it is found that localization allows the memory to be stable in the presence of a finite anyon density. Enhancements to this effect are also considered using random lattices, and similar problems for anyons transported by thermal errors are considered.

NANOGrav is a consortium of radio astronomers and gravitational wave physicists whose goal is to detect gravitational waves using an array of millisecond pulsars as clocks. Whereas interferometric gravitational wave experiments use lasers to create the long arms of the detector, NANOGrav uses earth-pulsar pairs. The limits that pulsar timing places on the energy density of gravitational waves in the universe are on the brink of limiting models of galaxy formation and have already placed limits on the tension of cosmic strings. Pulsar timing has traditionally focused on stochastic sources, but most recently I have been investigating the idea of detecting individual gravitational wave bursts wherein there are some interesting advantages. I will also demonstrate how the array can be used to reconstruct the waveform and obtain its direction.

The properties of a superfluid phase transition with a d-wave order parameter in a strongly interacting field theory with gravity dual are considered. In the context of the AdS/CFT correspondence, this amounts to writing down an action for a charged, massive spin two field on a background, and I will discuss all technical problems. In the second part I will show that coupling bulk fermions to the spin two field and studying the fermionic two-point function, one recovers interesting features of d-wave superconductors, like d-wave gap, Dirac nodes and Fermi arcs.

Nonlocality is arguably one of the most remarkable features of quantum mechanics. On the other hand nature seems to forbid other no-signaling correlations that cannot be generated by quantum systems. Usual approaches to explain this limitation is based on information theoretic properties of the correlations without any reference to physical theories they might emerge from. However, as shown in [PRL 104, 140401 (2010)], it is the structure of local quantum systems that determines the bipartite correlations possible in quantum mechanics. We investigate this connection further by introducing toy systems with regular polygons as local state spaces. This allows us to study the transition between bipartite classical, no-signaling and quantum correlations by modifying only the local state space. It turns out that the strength of nonlocality of the maximally entangled state depends crucially on a simple geometric property of the local state space, known as strong self-duality. We prove that the limitation of nonlocal correlations is a general result valid for the maximally entangled state in any model with strongly self-dual local state spaces, since such correlations must satisfy the principle of macroscopic locality. This implies notably that Tsirelson’s bound for correlations of the maximally entangled state in quantum mechanics can be regarded as a consequence of strong self-duality of local quantum systems. Finally, our results also show that there exist models which are locally almost identical to quantum mechanics, but can nevertheless generate maximally nonlocal correlations.

We derive a holographic dual description of free quantum field theory in arbitrary dimensions, by reinterpreting the exact renormalization group, to obtain a higher spin gravity theory of the general type which had been proposed and studied as a dual theory

We find analytic models that can perfectly transfer, without state initialization or remote collaboration, arbitrary functions in two- and three-dimensional interacting bosonic and fermionic networks. This provides for the possible experimental implementation of state transfer through bosonic or fermionic atoms trapped in optical lattices. A significant finding is that the state of a spin qubit can be perfectly transferred through a fermionic system. Families of Hamiltonians are described that are related to the linear models and that enable the perfect transfer of arbitrary functions. Furthermore, we propose methods for eliminating certain types of errors

Higher derivative extensions of the Standard Model are renormalizable but without a quadratic divergent higgs mass. Electroweak presision data constraint the scale of the higher derivatives to at least a few TeV, but then these models have no flavor problem. We skim through these and other interesting results, most remarkably causality as an emergent characteristic at long distances. But we start by explaining the indefinite metric quantization procedure proposed by Lee and Wick which is necessary for unitary.

More than forty years ago Nobel laureate P.W. Anderson studied the overlap between two nearby ground states. The result that the overlap tends to zero in the thermodynamics limit was catastrophic for those times. More recently the study of the overlap between ground states, i.e. the fidelity, led to the formulation of the so called fidelity approach to (quantum) phase transition (QPT). This new approach to QPT does not rely on the identification of order parameters or symmetry pattern; rathers it embodies the theory of phase transitions with an operational meaning in terms of measurements. Nowadays orthogonality of ground states is much less surprising. I will provide the general scaling behavior of the fidelity at regular and at critical points of the phase diagrams, Anderson's result being a particular case. These results are useful to many areas of theoretical physics. A related quantity extensively studied here, the fidelity susceptibility, is well known in various other contexts under different names. In metrology it is called quantum Fisher information; in the theory of adiabatic computation it represents the figure of merit for efficient computation; in yet another context it is known as (real part of) the Berry geometric tensor.

Theories with extra dimensions naturally give rise to a large landscape of vacua stabilized by flux. I will show that the fastest decay is a giant leap to a wildly distant minimum, in which many different fluxes discharge at once. Indeed, the fastest decay is frequently the giantest leap of all, where all the fluxes discharge at once, which destabilizes the extra dimensions and begets a bubble of nothing. Finally, I will discuss how these giant leaps are mediated by the nucleation of "monkey branes" that wrap the extra dimensions.

We will discuss two topics. First we will revisit the asymptotic structure of classical de Sitter space. In particular we will construct charges at future infinity (I^+) and obtain the asymptotic symmetry group drawing parallels with the BMS group of flat space. Secondly, move away from the region I^+ and study the space living near the cosmological horizon by considering large rotating Nariai black holes whose size tends to that of the cosmological horizon. We will examine the resulting near (cosmological) horizon geometry and find an interesting asymptotic structure containing the Virasoro algebra, suggestive of a holographic interpretation.